Abstract
We prove that if M is a 4-connected binary matroid and N is an internally 4-connected proper minor of M with at least 7 elements, then, unless M is a certain 16-element matroid, there is an element e of E(M) such that either M∖e or M/e is internally 4-connected having an N-minor. This strengthens a result of Zhou and is a first step towards obtaining a splitter theorem for internally 4-connected binary matroids.
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